A company is about to launch a new cell phone model. In the past, 40% of its cell phones have launched successfully. Before any cell phone is launched, the company conducts market research and receives a report predicting favorable or unfavorable sales. In the past, 70% of successful cell phones and 20% of unsuccessful cell phones received favorable reports.

What is the probability that the new cell phone will receive a favorable report, given that the cell phone launch is successful?

0.45
0.54
0.64
0.70

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nexlout nexlout · Answer 1 · 2016-09-04T16:12:43+02:00

The probability is 0.70

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virtuematane virtuematane · Answer 2 · 2019-03-07T10:52:51+01:00

Hence, the probability is:

0.70

Let x be the total cell phones.

Let A denote the event of cell phone will receive a favorable report.

B denote the event that the cell phone is launched successfully.

Now we have to find the probability:

P(A|B)

We know that P(A|B) is calculated as:

[tex]P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}[/tex]

Now it is given that:

40% of its cell phones have launched successfully.

i.e. [tex]P(B)=0.4x[/tex]

( Since,

[tex]\dfrac{40}{100}\times x=0.4x[/tex]

Also,

In the past, 70% of successful cell phones and 20% of unsuccessful cell phones received favorable reports.

So, Number of successfully launched+favorable cell phones is successful are:

40% of 70% of the total cell phones.

i.e.

[tex]P(A\bigcap B)=\dfrac{70}{100}\times \dfrac{40}{100}\times x[/tex]

Hence, the probability P(A|B) is:

[tex]\dfrac{\dfrac{40}{100}\times \dfrac{70}{100}\times x}{\dfrac{40}{100}\times x}\\\\\\\\=\dfrac{70}{100}=0.70[/tex][/tex]

Hence, the probability is:

0.70